Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
An activity making various patterns with 2 x 1 rectangular tiles.
This activity investigates how you might make squares and pentominoes from Polydron.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
My coat has three buttons. How many ways can you find to do up all
Investigate the different ways you could split up these rooms so
that you have double the number.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
What could the half time scores have been in these Olympic hockey
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
In how many ways can you stack these rods, following the rules?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you use the information to find out which cards I have used?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
How many models can you find which obey these rules?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?